The Real Reason Boruto Isn't Blessed With The Byakugan
After 700 chapters and 500 episodes, Naruto's expansive story came to an end. That wasn't it for the Naruto franchise, however. While Naruto as a series may have concluded, the adventures of the next generation of superpowered ninjas has been chronicled in Boruto, a direct sequel. Just like Naruto before it, Boruto bears the name of its titular character, who, in this case, is Naruto's son.
Appearing alongside Boruto are a number of other children of central characters from throughout Naruto's run. Many of the kids now featured in the series are capable of using powers similar or identical to those of their parents. For example, Sarada Uchiha is the daughter of Naruto's rival Sasuke Uchiha and Naruto's former teammate Sakura Haruno. She possesses both her mother's intelligence and the ability to use the Sharingan ability like Sasuke and many other Uchiha clan members.
Since Boruto is the child of Naruto and Hinata Uzumaki (formerly Hyuga), it stands to reason that he should be capable of powers utilized by both his mother and father in this same manner. While this remains true in most cases, Naruto is most notably lacking the Byakugan.
The ability that Kishimoto forgot
The Byakugan is a type of kekkei genkai, which is an umbrella term used to label magical abilities from inherited genetic traits rather than those that can be learned. Like the Uchiha clan's Sharingan, the Byakugan manifests in its bearer's eyes. However, whereas the Sharingan must be activated, the Byakugan permanently renders its bearer's eyes milky white and pupil-less. Thus, both Hinata and Neji, the members of the Hyuga clan to first appear in Naruto, possess eyes that are milky white and pupil-less at all times as evidence of their possessing the Byakugan.
Given that Boruto is a member of the Hyuga clan by merit of his mother's bloodline, he should theoretically have those same, distinct eyes. However, Boruto's eyes, rather, are blue and similar to Naruto's non-magical eyes in appearance. As it turns out, Naruto author Masashi Kishimoto once intended for Boruto to wield the Byakugan but simply forgot to draw the character with the Byakugan upon his first appearance in the Naruto manga.
Kishimoto corrected course to an extent later on in the series' run. Boruto at one point gains the power of celestial being Momoshiki. Sometimes, this can manifest in Momoshiki possessing Boruto's body entirely. In those moments, Boruto's right eye shifts into bearing the Byakugan's unique look. As the result of a simple mistake, therefore, Boruto's relationship with the Byakugan remains uniquely nonstandard for a descendent of the Hyuga clan.